No. In Jainism, Adinath (Rishabhanatha) is the first Tirthankar. The second Tirthankar is Ajitnath (Ajitanatha). Shiv (Shiva) is not recognized as a Tirthankar in Jain scriptures.

• Adinath is the first Tirthankar.
• Ajitnath is the second Tirthankar.
• There is no tradition in Jainism that identifies Shiv as the second Tirthankar; Shiv is a Hindu deity and outside the Jain Tirthankar lineage.

Both Digambar and Shwetambar traditions agree on Ajitnath as the second Tirthankar. You can read more here